Help Plane motions rolling wheel

[desistyle19]

Help! Plane motions rolling wheel

Hi there, I am not having any luck with this question at all and am hoping that there is someone out there that can help me out... here goes:

The below cyclinder rolls to the right at 10 in/sec. Determine the angular velocity of BC and CD

I am actually trying to prepare for a midterm and am not getting anywhere close to the answers that I am supposed to get.

I am using the following formulas: Vb= Vc/b + Vc
I know for the radius of Vb that would be 12" + 6"/2 = 9"

the biggest challenge for me I guess is when drawing the triangle, I am not getting the right angles, therefore, my answer is not correct.

 

[denverdoc]

Where is D in the figure? I get 1 rev/sec for BC.

 

[m2003]

Hello,

I understand that you are having trouble solving this problem and are looking for some assistance. Let me try to break down the problem for you.

First, we need to define the variables in the problem. Let's say that the cylinder has a radius of R and is rolling to the right at a velocity of Vb = 10 in/sec. The point of contact between the cylinder and the ground is at point C.

Now, we can use the formula Vb = Vc/b + Vc to solve for the angular velocity of BC and CD. Here, Vc/b represents the linear velocity of point C and Vc represents the linear velocity of the center of the cylinder.

To find Vc/b, we can use the formula Vc/b = ω × r, where ω is the angular velocity and r is the distance between point C and the center of the cylinder. In this case, r is equal to R/2 since the distance from the center to the point of contact is half the radius.

Now, we can plug in the values we have and solve for ω. We get Vc/b = ω × R/2, or ω = 2Vc/R.

To find Vc, we can use the formula Vc = Vb - Vc/b. Substituting in the values we have, we get Vc = 10 in/sec - 2Vc/R. Solving for Vc, we get Vc = 10R/3 in/sec.

Finally, we can use the formula Vc = ω × R to solve for the angular velocity of CD. Substituting in the values we have, we get 10R/3 in/sec = ω × R. Solving for ω, we get ω = 10/3 rad/sec.

I hope this helps you solve the problem and prepare for your midterm. Remember to double check your calculations and units to ensure accuracy. Good luck!